Problem 1E

1. Suppose $\Sigma a_{n}$ and $\Sigma b_{n}$ are series with positive terms and $\Sigma b_{n}$ is known to be convergent.

(a) If $a_{n}>b_{n}$ for all $n$, what can you say about $\Sigma a_{n}$ ? Why?

(b) If $a_{n}<b_{n}$ for all $n$, what can you say about $\sum a_{n}$ ? Why?